In [404]:
!pip install pandas matplotlib numpy statsmodels seaborn scipy -q

[notice] A new release of pip is available: 24.3.1 -> 25.1.1
[notice] To update, run: pip install --upgrade pip
In [405]:
# Import all datasets for sit to stand
import pandas as pd
from data_collector import get_sit_to_stand_paths, get_sit_to_stand_challenge_paths, get_water_task_paths, get_water_task_challenge_paths, get_step_count_paths, get_step_count_challenge_paths
import numpy as np

task = 'sit2stand'
if task == 'sit2stand':
    paths_standard = get_sit_to_stand_paths()
    paths_challenge = get_sit_to_stand_challenge_paths()
elif task == 'water':
    paths_standard = get_water_task_paths()
    paths_challenge = get_water_task_challenge_paths()
elif task == 'step_count':
    paths_standard = get_step_count_paths()
    paths_challenge = get_step_count_challenge_paths()


dfs_stand = [pd.read_csv(path) for path in paths_standard]
dfs_stand_challenge = [pd.read_csv(path) for path in paths_challenge]

# For each dataframe, add a new column 'time_s' which is the time in seconds from the first timestamp
for df in dfs_stand:
    df['time_s'] = (df['timestamp_ms'] - df['timestamp_ms'].min()) / 1000


for df in dfs_stand_challenge:
    df['time_s'] = (df['timestamp_ms'] - df['timestamp_ms'].min()) / 1000

if task=='step_count':
    # rename column from acceleration_m/s²_x to 'freeAcceleration_m/s²_x' for x y and z
    dfs_stand = [df.rename(columns={'acceleration_m/s²_x': 'freeAcceleration_m/s²_x', 'acceleration_m/s²_y': 'freeAcceleration_m/s²_y', 'acceleration_m/s²_z': 'freeAcceleration_m/s²_z'}) for df in dfs_stand]
    dfs_stand_challenge = [df.rename(columns={'acceleration_m/s²_x': 'freeAcceleration_m/s²_x', 'acceleration_m/s²_y': 'freeAcceleration_m/s²_y', 'acceleration_m/s²_z': 'freeAcceleration_m/s²_z'}) for df in dfs_stand_challenge]

# Calculate magnitude of acceleration 
for df in dfs_stand:
    df['acceleration_magnitude'] = np.sqrt(
        df['freeAcceleration_m/s²_x']**2 + 
        df['freeAcceleration_m/s²_y']**2 + 
        df['freeAcceleration_m/s²_z']**2
    )

for df in dfs_stand_challenge:
    df['acceleration_magnitude'] = np.sqrt(
        df['freeAcceleration_m/s²_x']**2 + 
        df['freeAcceleration_m/s²_y']**2 + 
        df['freeAcceleration_m/s²_z']**2
    )


df_standard = dfs_stand[0]
df_challenge = dfs_stand_challenge[0]

print(f"Using data from {paths_standard[0]} and {paths_challenge[0]}")

Data directory to look in: /Users/ashish/Desktop/DS4W/sensorhub-analysis/data
Sub directories for each Device ID found: ['f3eba7e5-dbda-4f4c-9fa8-8e8308b334f6', '5f680dfb-2510-4790-8f10-cb8724e7004c', '3c2d2423-8ac8-4a8c-95e2-aba5cc14abf8']
Data directory to look in: /Users/ashish/Desktop/DS4W/sensorhub-analysis/data
Sub directories for each Device ID found: ['f3eba7e5-dbda-4f4c-9fa8-8e8308b334f6', '5f680dfb-2510-4790-8f10-cb8724e7004c', '3c2d2423-8ac8-4a8c-95e2-aba5cc14abf8']
Using data from /Users/ashish/Desktop/DS4W/sensorhub-analysis/data/3c2d2423-8ac8-4a8c-95e2-aba5cc14abf8/csv/Recordings_Signal_Data/2025-05-08T12_59_06Z-sit_to_stand/sit_to_stand_imu.csv and /Users/ashish/Desktop/DS4W/sensorhub-analysis/data/3c2d2423-8ac8-4a8c-95e2-aba5cc14abf8/csv/Recordings_Signal_Data/2025-05-12T06_58_28Z-sit_to_stand_challenge/sit_to_stand_imu.csv

Experimental Design¶

  • Within-subject study: Each participant (N = 5) performs:

    • Sit-to-stand under normal conditions
    • Sit-to-stand while doing a cognitive task (serial subtraction)

  • Data collected:

    • Timestamped acceleration on 3 axes (x, y, z) for ~30 seconds per trial

Step 1: Compute Acceleration Magnitude¶

We reduce the 3D accelerometer signal into a single scalar by computing the magnitude of free acceleration at each time point:

$$ \text{acc_mag}(t) = \sqrt{x_t^2 + y_t^2 + z_t^2} $$

This gives us a time-series that reflects total body movement intensity.

Step 2: Feature Extraction : Mean Acceleration¶

We summarize the signal for each trial (one per participant per condition) by computing the mean acceleration magnitude:

$$ \bar{a} = \frac{1}{T} \sum_{t=1}^{T} \text{acc_mag}(t) $$

Where:

  • T is the number of time points in the trial
  • a' represents the average movement intensity

🔍 Step 3: Statistical Testing : Paired t-test¶

To assess whether the cognitive condition affects mean acceleration, we compare the values within participants using a paired t-test.

Let the difference for each participant be:

$$ D_i = a_{\text{normal},i} - a_{\text{cognitive},i} $$

We test the null hypothesis:

$$ H_0: \mu_D = 0 \quad \text{(no difference)} $$

With the t-statistic:

$$ t = \frac{\bar{D}}{s_D / \sqrt{n}} $$

Where:

  • D' is the mean of the differences
  • s_D is the standard deviation of the differences
  • n is the number of participants

If the resulting p-value < 0.05, we reject ( H_0 ), concluding that cognitive load significantly alters movement.

In [406]:
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from datetime import datetime

# Convert timestamps to datetime for better x-axis labels
# Create a relative time in seconds from the first timestamp
def visualize_data(df):
    # Plot the acceleration data
    plt.figure(figsize=(12, 8))

    # Plot each axis
    plt.subplot(3, 1, 1)
    plt.plot(df['time_s'], df['freeAcceleration_m/s²_x'], 'r-', label='X-axis')
    plt.ylabel('Acceleration (m/s²)')
    plt.title('Free Acceleration X-axis')
    plt.grid(True)
    plt.legend()

    plt.subplot(3, 1, 2)
    plt.plot(df['time_s'], df['freeAcceleration_m/s²_y'], 'g-', label='Y-axis')
    plt.ylabel('Acceleration (m/s²)')
    plt.title('Free Acceleration Y-axis')
    plt.grid(True)
    plt.legend()

    plt.subplot(3, 1, 3)
    plt.plot(df['time_s'], df['freeAcceleration_m/s²_z'], 'b-', label='Z-axis')
    plt.xlabel('Time (seconds)')
    plt.ylabel('Acceleration (m/s²)')
    plt.title('Free Acceleration Z-axis')
    plt.grid(True)
    plt.legend()

    plt.tight_layout()
    plt.show()

    # Combined view of all three axes
    plt.figure(figsize=(12, 6))
    plt.plot(df['time_s'], df['freeAcceleration_m/s²_x'], 'r-', label='X-axis')
    plt.plot(df['time_s'], df['freeAcceleration_m/s²_y'], 'g-', label='Y-axis')
    plt.plot(df['time_s'], df['freeAcceleration_m/s²_z'], 'b-', label='Z-axis')
    plt.xlabel('Time (seconds)')
    plt.ylabel('Acceleration (m/s²)')
    plt.title('Free Acceleration - All Axes')
    plt.grid(True)
    plt.legend()
    plt.tight_layout()
    plt.show()

    # Plot the magnitude
    plt.figure(figsize=(12, 5))
    plt.plot(df['time_s'], df['acceleration_magnitude'], 'k-')
    plt.xlabel('Time (seconds)')
    plt.ylabel('Acceleration Magnitude (m/s²)')
    plt.title('Magnitude of Acceleration')
    plt.grid(True)
    plt.tight_layout()
    plt.show()
In [407]:
# Visualize normal data
visualize_data(df_standard)
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In [408]:
# Visualize challenge data
visualize_data(df_challenge)
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In [409]:
# Compare both data x-axis acceleration
def compare_acceleration_x(df, df_challenge):
    plt.figure(figsize=(12, 6))
    plt.plot(df['time_s'], df['freeAcceleration_m/s²_x'], 'r-', label='Normal')
    plt.plot(df_challenge['time_s'], df_challenge['freeAcceleration_m/s²_x'], 'b-', label='Challenge')
    plt.xlabel('Time (seconds)')
    plt.ylabel('Acceleration (m/s²)')
    plt.title('X-axis Acceleration Comparison')
    plt.legend()
    plt.show()

# Compare both data x-axis acceleration
compare_acceleration_x(df_standard, df_challenge)
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In [410]:
# Compare both data y-axis acceleration
def compare_acceleration_y(df, df_challenge):
    plt.figure(figsize=(12, 6))
    plt.plot(df['time_s'], df['freeAcceleration_m/s²_y'], 'r-', label='Normal')
    plt.plot(df_challenge['time_s'], df_challenge['freeAcceleration_m/s²_y'], 'b-', label='Challenge')
    plt.xlabel('Time (seconds)')
    plt.ylabel('Acceleration (m/s²)')
    plt.title('Y-axis Acceleration Comparison')
    plt.legend()
    plt.show()

# Compare both data y-axis acceleration
compare_acceleration_y(df_standard, df_challenge)
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In [411]:
# Compare both data z-axis acceleration
def compare_acceleration_z(df, df_challenge):
    plt.figure(figsize=(12, 6))
    plt.plot(df['time_s'], df['freeAcceleration_m/s²_z'], 'r-', label='Normal')
    plt.plot(df_challenge['time_s'], df_challenge['freeAcceleration_m/s²_z'], 'b-', label='Challenge')
    plt.xlabel('Time (seconds)')
    plt.ylabel('Acceleration (m/s²)')
    plt.title('Y-axis Acceleration Comparison')
    plt.legend()
    plt.show()

# Compare both data z-axis acceleration
compare_acceleration_z(df_standard, df_challenge)
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In [412]:
# Compare both data magnitude of acceleration
def compare_acceleration_magnitude(df, df_challenge):
    plt.figure(figsize=(12, 6))
    plt.plot(df['time_s'], df['acceleration_magnitude'], 'r-', label='Normal')
    plt.plot(df_challenge['time_s'], df_challenge['acceleration_magnitude'], 'b-', label='Challenge')
    plt.xlabel('Time (seconds)')
    plt.ylabel('Acceleration Magnitude (m/s²)')
    plt.title('Magnitude of Acceleration Comparison')
    plt.legend()
    plt.show()

# Compare both data magnitude of acceleration
compare_acceleration_magnitude(df_standard, df_challenge)
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In [413]:
# Compare x-acceleration across all participants
def compare_acceleration_x_all(dfs, axis='x'):
    plt.figure(figsize=(20, 6))
    for i, df in enumerate(dfs):
        plt.plot(df['time_s'], df[f'freeAcceleration_m/s²_{axis}'], label=f'Participant {i+1}')
    plt.xlabel('Time (seconds)')
    plt.ylabel('Acceleration (m/s²)')
    plt.title(f'{axis}-axis Acceleration Comparison')

    plt.legend()
    plt.show()


# Compare x-acceleration across all participants
compare_acceleration_x_all(dfs_stand)

# Compare x-acceleration across all participants
compare_acceleration_x_all(dfs_stand, 'y')

# Compare x-acceleration across all participants
compare_acceleration_x_all(dfs_stand, 'z')
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In [414]:
# Compare x-acceleration across all participants
compare_acceleration_x_all(dfs_stand_challenge, 'x')

# Compare x-acceleration across all participants
compare_acceleration_x_all(dfs_stand_challenge, 'y')

# Compare x-acceleration across all participants
compare_acceleration_x_all(dfs_stand_challenge, 'z')
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In [415]:
len(dfs_stand), dfs_stand
Out[415]:
(5,
 [       timestamp_ms  timestamp_μs  freeAcceleration_m/s²_x  \
  0     1746709146601     231101705                -0.390118   
  1     1746709146618     231118372                -0.103113   
  2     1746709146634     231135039                 0.693871   
  3     1746709146651     231151706                 0.976024   
  4     1746709146668     231168373                 0.641669   
  ...             ...           ...                      ...   
  1778  1746709176235     260735631                 0.444211   
  1779  1746709176252     260752298                 0.499439   
  1780  1746709176268     260768965                 0.407235   
  1781  1746709176285     260785632                 0.912732   
  1782  1746709176302     260802299                 1.244095   
  
        freeAcceleration_m/s²_y  freeAcceleration_m/s²_z  time_s  \
  0                   -0.076349                -1.039129   0.000   
  1                    0.163044                -1.324339   0.017   
  2                    0.050779                -0.537230   0.033   
  3                   -0.223424                -0.630582   0.050   
  4                   -0.208525                -1.296504   0.067   
  ...                       ...                      ...     ...   
  1778                -0.166851                -1.083000  29.634   
  1779                 1.436913                -1.265997  29.651   
  1780                 1.634014                -0.130795  29.667   
  1781                 0.923709                -0.212215  29.684   
  1782                -0.191012                -0.058644  29.701   
  
        acceleration_magnitude  
  0                   1.112569  
  1                   1.338316  
  2                   0.879006  
  3                   1.183290  
  4                   1.461555  
  ...                      ...  
  1778                1.182392  
  1779                1.979117  
  1780                1.689068  
  1781                1.315810  
  1782                1.260038  
  
  [1783 rows x 7 columns],
         timestamp_ms  timestamp_μs  freeAcceleration_m/s²_x  \
  0     1746708388926     199427346                 0.046509   
  1     1746708388943     199444013                 0.040232   
  2     1746708388959     199460680                 0.031789   
  3     1746708388976     199477347                 0.140357   
  4     1746708388993     199494014                -0.065061   
  ...             ...           ...                      ...   
  1786  1746708418693     229194608                -0.498794   
  1787  1746708418710     229211275                -0.424106   
  1788  1746708418727     229227942                -0.571897   
  1789  1746708418743     229244609                -0.149889   
  1790  1746708418760     229261276                -0.270612   
  
        freeAcceleration_m/s²_y  freeAcceleration_m/s²_z  time_s  \
  0                   -0.049324                 0.378253   0.000   
  1                   -0.082570                 0.300064   0.017   
  2                   -0.056001                 0.414821   0.033   
  3                    0.047952                 0.457452   0.050   
  4                   -0.023433                 0.105056   0.067   
  ...                       ...                      ...     ...   
  1786                -0.210728                -2.165378  29.767   
  1787                -0.477301                -1.594980  29.784   
  1788                -0.815092                -1.692597  29.801   
  1789                -1.471216                -2.034573  29.817   
  1790                -1.605592                -1.728581  29.834   
  
        acceleration_magnitude  
  0                   0.384280  
  1                   0.313807  
  2                   0.419789  
  3                   0.480897  
  4                   0.125773  
  ...                      ...  
  1786                2.232054  
  1787                1.718035  
  1788                1.963754  
  1789                2.515240  
  1790                2.374690  
  
  [1791 rows x 7 columns],
         timestamp_ms  timestamp_μs  freeAcceleration_m/s²_x  \
  0     1747033013617     123566622                 0.092350   
  1     1747033013634     123583289                 0.308911   
  2     1747033013650     123599956                 0.478206   
  3     1747033013667     123616623                 0.230824   
  4     1747033013684     123633290                -0.022896   
  ...             ...           ...                      ...   
  1783  1747033043334     153283883                 0.467967   
  1784  1747033043351     153300550                 0.476856   
  1785  1747033043368     153317217                 0.809446   
  1786  1747033043384     153333884                 1.358585   
  1787  1747033043401     153350551                 1.458225   
  
        freeAcceleration_m/s²_y  freeAcceleration_m/s²_z  time_s  \
  0                    0.311271                -0.020087   0.000   
  1                    0.240814                -0.048132   0.017   
  2                    0.176104                 0.521458   0.033   
  3                    0.107216                 0.944909   0.050   
  4                   -0.292477                 1.117781   0.067   
  ...                       ...                      ...     ...   
  1783                -0.123759                 0.294951  29.717   
  1784                -0.192136                 0.000191  29.734   
  1785                -0.279738                 0.055799  29.751   
  1786                -0.082746                 0.192875  29.767   
  1787                 0.042822                -0.078331  29.784   
  
        acceleration_magnitude  
  0                   0.325302  
  1                   0.394632  
  2                   0.729117  
  3                   0.978585  
  4                   1.155639  
  ...                      ...  
  1783                0.566838  
  1784                0.514109  
  1785                0.858236  
  1786                1.374700  
  1787                1.460955  
  
  [1788 rows x 7 columns],
         timestamp_ms  timestamp_μs  freeAcceleration_m/s²_x  \
  0     1746704814859     209719360                 0.047203   
  1     1746704814876     209736027                 0.038527   
  2     1746704814892     209752694                 0.040116   
  3     1746704814909     209769361                 0.015788   
  4     1746704814926     209786028                 0.013383   
  ...             ...           ...                      ...   
  1782  1746704844560     239419954                 1.038621   
  1783  1746704844576     239436621                 1.016820   
  1784  1746704844593     239453288                 1.064942   
  1785  1746704844610     239469955                 1.247072   
  1786  1746704844626     239486622                 1.264108   
  
        freeAcceleration_m/s²_y  freeAcceleration_m/s²_z  time_s  \
  0                   -0.167005                 0.283479   0.000   
  1                   -0.128904                 0.256366   0.017   
  2                   -0.065615                 0.185970   0.033   
  3                    0.011174                 0.267086   0.050   
  4                    0.116792                 0.386025   0.067   
  ...                       ...                      ...     ...   
  1782                -0.952962                -1.862821  29.701   
  1783                -0.380841                -0.648541  29.717   
  1784                -0.680544                -0.057891  29.734   
  1785                -0.734097                 0.777641  29.751   
  1786                -1.198298                 1.096929  29.767   
  
        acceleration_magnitude  
  0                   0.332384  
  1                   0.289524  
  2                   0.201245  
  3                   0.267786  
  4                   0.403528  
  ...                      ...  
  1782                2.336016  
  1783                1.264740  
  1784                1.265145  
  1785                1.642807  
  1786                2.058431  
  
  [1787 rows x 7 columns],
         timestamp_ms  timestamp_μs  freeAcceleration_m/s²_x  \
  0     1747033772226     882164663                -0.323900   
  1     1747033772243     882181330                -0.362763   
  2     1747033772259     882197997                -0.291865   
  3     1747033772276     882214664                -0.151857   
  4     1747033772293     882231331                 0.109761   
  ...             ...           ...                      ...   
  1780  1747033801893     911831923                -1.488138   
  1781  1747033801910     911848590                -1.426718   
  1782  1747033801927     911865257                -1.696018   
  1783  1747033801943     911881924                -1.953311   
  1784  1747033801960     911898591                -1.848742   
  
        freeAcceleration_m/s²_y  freeAcceleration_m/s²_z  time_s  \
  0                    0.258127                -0.177178   0.000   
  1                    0.430727                -0.244325   0.017   
  2                    0.627431                -0.266001   0.033   
  3                    0.743734                -0.228697   0.050   
  4                    0.631557                -0.220694   0.067   
  ...                       ...                      ...     ...   
  1780                 0.771571                -2.830918  29.667   
  1781                 0.979907                -2.799942  29.684   
  1782                 0.627168                -2.471069  29.701   
  1783                 0.224583                -1.783616  29.717   
  1784                 0.127890                -1.260719  29.734   
  
        acceleration_magnitude  
  0                   0.450480  
  1                   0.613855  
  2                   0.741357  
  3                   0.792782  
  4                   0.677951  
  ...                      ...  
  1780                3.289981  
  1781                3.291719  
  1782                3.062026  
  1783                2.654646  
  1784                2.241342  
  
  [1785 rows x 7 columns]])
In [416]:
# Compare number of rows in each participant's data by plotting
import matplotlib.pyplot as plt

# Create a list to store the number of rows for each participant
num_rows_list_standard = [len(df) for df in dfs_stand]
num_rows_list_challenge = [len(df) for df in dfs_stand_challenge]

# PLot bar chart of number of rows for each participant with participant number on x-axis
plt.figure(figsize=(14, 6))
plt.bar(range(len(num_rows_list_standard)), num_rows_list_standard, label='Standard')
# Label each bar with the number of samples in the participant's data 
for i, num_rows in enumerate(num_rows_list_standard):
    plt.text(i, num_rows, str(num_rows), ha='center', va='bottom')
plt.xlabel('Participant')
plt.ylabel('Number of Rows')
plt.title('Number of Rows in Each Participant in Standard Task')
plt.legend()
Out[416]:
<matplotlib.legend.Legend at 0x140ee20e0>
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In [417]:
plt.figure(figsize=(12, 6))
plt.bar(range(len(num_rows_list_challenge)), num_rows_list_challenge, label='Challenge')
for i, num_rows in enumerate(num_rows_list_challenge):
    plt.text(i, num_rows, str(num_rows), ha='center', va='bottom')
plt.xlabel('Participant')
plt.ylabel('Number of Rows')
plt.title('Number of Rows in Each Participant in Challenge Task')
plt.legend()
Out[417]:
<matplotlib.legend.Legend at 0x140ee3d00>
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In [418]:
# Plot a double, non overlapping bar chart of number of rows for standard and challenge tasks
count_df = pd.DataFrame({
    'Standard': num_rows_list_standard,
    'Challenge': num_rows_list_challenge
})
count_df.plot(kind='bar', figsize=(12, 6))
plt.xlabel('Participant')
plt.ylabel('Number of Rows')
plt.title('Number of Rows in Each Participant in Standard and Challenge Tasks')
plt.legend()
Out[418]:
<matplotlib.legend.Legend at 0x140f47760>
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In [419]:
# Calculate mean acceleration for each axis per participant 
mean_acceleration_standard_x = [df['freeAcceleration_m/s²_x'].mean() for df in dfs_stand]
mean_acceleration_challenge_x = [df['freeAcceleration_m/s²_x'].mean() for df in dfs_stand_challenge]
mean_acceleration_standard_y = [df['freeAcceleration_m/s²_y'].mean() for df in dfs_stand]
mean_acceleration_challenge_y = [df['freeAcceleration_m/s²_y'].mean() for df in dfs_stand_challenge]
mean_acceleration_standard_z = [df['freeAcceleration_m/s²_z'].mean() for df in dfs_stand]
mean_acceleration_challenge_z = [df['freeAcceleration_m/s²_z'].mean() for df in dfs_stand_challenge]

# Plot and compare mean acceleration for each axis per participant
def plot_mean_acceleration(mean_acceleration_standard, mean_acceleration_challenge, axis='x'):
    plt.figure(figsize=(12, 6))
    plt.bar(range(len(mean_acceleration_standard)), mean_acceleration_standard, label='Standard')
    plt.bar(range(len(mean_acceleration_challenge)), mean_acceleration_challenge, label='Challenge')
    # Label each bar with the mean acceleration, rounded to 2 decimal places
    for i, mean_acceleration in enumerate(mean_acceleration_standard):
        # write text in blue color
        plt.text(i, mean_acceleration, str(round(mean_acceleration, 4)), ha='center', va='bottom', color='blue')
    for i, mean_acceleration in enumerate(mean_acceleration_challenge_x):
        plt.text(i, mean_acceleration, str(round(mean_acceleration, 4)), ha='center', va='bottom', color='black')
    plt.xlabel('Participant')
    plt.ylabel(f"Mean Acceleration in {axis}-axis (m/s²)")
    plt.title('Mean Acceleration in Standard and Challenge Tasks')
    plt.legend()
In [420]:
# Mean acceleration for x axis
plot_mean_acceleration(mean_acceleration_standard_x, mean_acceleration_challenge_x, 'x')
No description has been provided for this image
In [421]:
# Mean acceleration for y axis
plot_mean_acceleration(mean_acceleration_standard_y, mean_acceleration_challenge_y, 'y')
No description has been provided for this image
In [422]:
# Mean acceleration for z axis
plot_mean_acceleration(mean_acceleration_standard_z, mean_acceleration_challenge_z, 'z')
No description has been provided for this image
In [423]:
# Plot sample means using qq plots
import statsmodels.api as sm

# Create a list to store the sample means for each participant
sample_means_standard_x = np.array([df['freeAcceleration_m/s²_x'].mean() for df in dfs_stand])
sample_means_challenge_x = np.array([df['freeAcceleration_m/s²_x'].mean() for df in dfs_stand_challenge])
sample_means_standard_y = np.array([df['freeAcceleration_m/s²_y'].mean() for df in dfs_stand])
sample_means_challenge_y = np.array([df['freeAcceleration_m/s²_y'].mean() for df in dfs_stand_challenge])
sample_means_standard_z = np.array([df['freeAcceleration_m/s²_z'].mean() for df in dfs_stand])
sample_means_challenge_z = np.array([df['freeAcceleration_m/s²_z'].mean() for df in dfs_stand_challenge])

fig, axs = plt.subplots(2, 3, figsize=(20, 12), sharex=True)


# Plot qq plot of sample means and add labels
sm.qqplot(sample_means_standard_x, line='45', fit=True, ax=axs[0, 0])
axs[0, 0].set_xlabel('Theoretical Quantiles')
axs[0, 0].set_ylabel('Sample Quantiles')
axs[0, 0].set_title('QQ Plot of Sample Means for Standard Task along x-axis')
axs[0, 0].legend()

# Plot qq plot of sample means
sm.qqplot(sample_means_challenge_x, line='45', fit=True, ax=axs[1, 0])
axs[1, 0].set_xlabel('Theoretical Quantiles')
axs[1, 0].set_ylabel('Sample Quantiles')
axs[1, 0].set_title('QQ Plot of Sample Means for Challenge Task along x-axis')
axs[1, 0].legend()

# Plot qq plot of sample means
sm.qqplot(sample_means_standard_y, line='45', fit=True, ax=axs[0, 1])
axs[0, 1].set_xlabel('Theoretical Quantiles')
axs[0, 1].set_ylabel('Sample Quantiles')
axs[0, 1].set_title('QQ Plot of Sample Means for Standard Task along y-axis')
axs[0, 1].legend()

# Plot qq plot of sample means
sm.qqplot(sample_means_challenge_y, line='45', fit=True, ax=axs[1, 1])
axs[1, 1].set_xlabel('Theoretical Quantiles')
axs[1, 1].set_ylabel('Sample Quantiles')
axs[1, 1].set_title('QQ Plot of Sample Means for Challenge Task along y-axis')
axs[1, 1].legend()

# Plot qq plot of sample means
sm.qqplot(sample_means_standard_z, line='45', fit=True, ax=axs[0, 2])
axs[0, 2].set_xlabel('Theoretical Quantiles')
axs[0, 2].set_ylabel('Sample Quantiles')
axs[0, 2].set_title('QQ Plot of Sample Means for Standard Task along z-axis')
axs[0, 2].legend()

# Plot qq plot of sample means
sm.qqplot(sample_means_challenge_z, line='45', fit=True, ax=axs[1, 2])
axs[1, 2].set_xlabel('Theoretical Quantiles')
axs[1, 2].set_ylabel('Sample Quantiles')
axs[1, 2].set_title('QQ Plot of Sample Means for Challenge Task along z-axis')
axs[1, 2].legend()

/var/folders/zp/3681gr8x5mg9vt0z3xbtlzx00000gn/T/ipykernel_91614/3602491626.py:20: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.
  axs[0, 0].legend()
/var/folders/zp/3681gr8x5mg9vt0z3xbtlzx00000gn/T/ipykernel_91614/3602491626.py:27: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.
  axs[1, 0].legend()
/var/folders/zp/3681gr8x5mg9vt0z3xbtlzx00000gn/T/ipykernel_91614/3602491626.py:34: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.
  axs[0, 1].legend()
/var/folders/zp/3681gr8x5mg9vt0z3xbtlzx00000gn/T/ipykernel_91614/3602491626.py:41: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.
  axs[1, 1].legend()
/var/folders/zp/3681gr8x5mg9vt0z3xbtlzx00000gn/T/ipykernel_91614/3602491626.py:48: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.
  axs[0, 2].legend()
/var/folders/zp/3681gr8x5mg9vt0z3xbtlzx00000gn/T/ipykernel_91614/3602491626.py:55: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.
  axs[1, 2].legend()
Out[423]:
<matplotlib.legend.Legend at 0x14122a6e0>
No description has been provided for this image
In [424]:
# Calculate magnitude of acceleration for each participant
mean_acceleration_standard_magnitude = np.array([df['acceleration_magnitude'].mean() for df in dfs_stand])
mean_acceleration_challenge_magnitude = np.array([df['acceleration_magnitude'].mean() for df in dfs_stand_challenge])

mean_acceleration_standard_magnitude, mean_acceleration_challenge_magnitude
Out[424]:
(array([1.78488787, 1.63689184, 1.39231585, 1.35709055, 1.45023621]),
 array([1.00407051, 1.23304809, 1.15220116, 0.69327856, 0.78111748]))
In [425]:
# Plot qq plot for mean acceleration of standard and challenge tasks
fig, axs = plt.subplots(1, 2, figsize=(20, 4), sharex=True)
# Plot qq plot for the mean magnitude of acceleration for standard and challenge tasks
sm.qqplot(mean_acceleration_standard_magnitude, line='45', fit=True, ax=axs[0])
axs[0].set_xlabel('Theoretical Quantiles')
axs[0].set_ylabel('Sample Quantiles')
axs[0].set_title('QQ Plot of Mean Magnitude of Acceleration for Standard Task')
axs[0].legend()

sm.qqplot(mean_acceleration_challenge_magnitude, line='45', fit=True, ax=axs[1])
axs[1].set_xlabel('Theoretical Quantiles')
axs[1].set_ylabel('Sample Quantiles')
axs[1].set_title('QQ Plot of Mean Magnitude of Acceleration for Challenge Task')
axs[1].legend()

/var/folders/zp/3681gr8x5mg9vt0z3xbtlzx00000gn/T/ipykernel_91614/205138737.py:8: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.
  axs[0].legend()
/var/folders/zp/3681gr8x5mg9vt0z3xbtlzx00000gn/T/ipykernel_91614/205138737.py:14: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.
  axs[1].legend()
Out[425]:
<matplotlib.legend.Legend at 0x141433370>
No description has been provided for this image
In [426]:
# Plot ecdf of sample means
import seaborn as sns

# Plot ecdf of sample means using subplots of grid 1,3 along x, y and z axis
fig, axs = plt.subplots(1, 3, figsize=(20, 6), sharex=True)
sns.ecdfplot(sample_means_standard_x, label='Standard', ax=axs[0])
sns.ecdfplot(sample_means_challenge_x, label='Challenge', ax=axs[0])
axs[0].set_xlabel('Mean Acceleration along x-axis (m/s²)')
axs[0].set_ylabel('ECDF')
axs[0].set_title('ECDF of Sample Means for Standard and Challenge Tasks')
axs[0].legend()

sns.ecdfplot(sample_means_standard_y, label='Standard', ax=axs[1])
sns.ecdfplot(sample_means_challenge_y, label='Challenge', ax=axs[1])
axs[1].set_xlabel('Mean Acceleration along y-axis (m/s²)')
axs[1].set_ylabel('ECDF')
axs[1].set_title('ECDF of Sample Means for Standard and Challenge Tasks')
axs[1].legend()

sns.ecdfplot(sample_means_standard_z, label='Standard', ax=axs[2])
sns.ecdfplot(sample_means_challenge_z, label='Challenge', ax=axs[2])
axs[2].set_xlabel('Mean Acceleration along z-axis (m/s²)')
axs[2].set_ylabel('ECDF')
axs[2].set_title('ECDF of Sample Means for Standard and Challenge Tasks')
axs[2].legend()
Out[426]:
<matplotlib.legend.Legend at 0x14111bd00>
No description has been provided for this image
In [427]:
fig, axs = plt.subplots(1, 2, figsize=(20, 4), sharex=True)

sns.ecdfplot(mean_acceleration_standard_magnitude, label='Standard', ax=axs[0])
sns.ecdfplot(mean_acceleration_challenge_magnitude, label='Challenge', ax=axs[1])
axs[0].set_xlabel('Mean Acceleration (m/s²)')
axs[0].set_ylabel('ECDF')
axs[0].set_title('ECDF of Mean Magnitude of Acceleration for Standard Task')
axs[0].legend()

axs[1].set_xlabel('Mean Acceleration (m/s²)')
axs[1].set_ylabel('ECDF')
axs[1].set_title('ECDF of Mean Magnitude of Acceleration for Challenge Task')
axs[1].legend()
Out[427]:
<matplotlib.legend.Legend at 0x1410ff730>
No description has been provided for this image
In [428]:
# Perform t-test for the magnitude of mean acceleration of standard and challenge tasks
mean_acc_standard = [df['acceleration_magnitude'].mean() for df in dfs_stand]
mean_acc_challenge = [df['acceleration_magnitude'].mean() for df in dfs_stand_challenge]

print(mean_acc_standard)
print(mean_acc_challenge)

[np.float64(1.7848878692954853), np.float64(1.636891837767239), np.float64(1.3923158522778347), np.float64(1.3570905500926835), np.float64(1.4502362050831268)]
[np.float64(1.0040705073076044), np.float64(1.2330480911660822), np.float64(1.1522011601310023), np.float64(0.6932785640948899), np.float64(0.7811174815974915)]
In [429]:
# Plot the magnitude of acceleration for each participant as a scatter plot
import matplotlib.pyplot as plt

participants = range(1, len(mean_acc_challenge) + 1)

plt.scatter(participants, mean_acc_standard, label='Standard')
plt.scatter(participants, mean_acc_challenge, label='Challenge')
Out[429]:
<matplotlib.collections.PathCollection at 0x140df6020>
No description has been provided for this image
In [430]:
# Plot a bar chart of mean acceleration of standard and challenge tasks
participants = range(1, len(mean_acc_challenge) + 1)

plt.plot(participants, mean_acc_standard, marker='o', label='Standard')
plt.plot(participants, mean_acc_challenge, marker='o', label='Challenge')
plt.xlabel("Participant")
plt.ylabel("Mean Acceleration Magnitude")
plt.title("Sit-to-Stand: Standard vs Challenge")
plt.legend()
plt.grid(True)
plt.show()
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In [431]:
# Paired t-test for the magnitude of mean acceleration of standard and challenge tasks
from scipy.stats import ttest_rel

t_stat, p_value = ttest_rel(mean_acc_standard, mean_acc_challenge)
print("Paired t-test result: \n")
print(f"t-statistic = {t_stat:.4f}")
print(f"p-value = {p_value:.4f}")

Paired t-test result: 

t-statistic = 5.5460
p-value = 0.0052
In [432]:
# Conclusion

print("Conclusion:")
print("*"*30)
if p_value < 0.05:
    print("There is a significant difference in the mean acceleration magnitude between the standard and challenge tasks.")
else:
    print("There is no significant difference in the mean acceleration magnitude between the standard and challenge tasks.")

Conclusion:
******************************
There is a significant difference in the mean acceleration magnitude between the standard and challenge tasks.
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